Fluctuations of the SNR at the wiener filter output for large dimensional signals

Consider the linear Wiener receiver for multidimensional signals. Such a receiver is frequently encountered in wireless communications and in array processing, and the Signal to noise ratio (SNR) at its output is a popular performance index. The SNR can be modeled as a random quadratic form and in order to study this quadratic form, one can rely on well-know results in Random Matrix Theory, if one assumes that the dimension of the received and transmitted signals go to infinity, their ratio remaining constant. In this paper, we study the asymptotic behavior of the SNR for a large class of multidimensional signals (MIMO, CDMA, MC-CDMA transmissions). More precisely, we provide a deterministic approximation of the SNR, that depends on the system parameters; furthermore, the fluctuations of the SNR around this deterministic approximation are shown to be Gaussian, with variance decreasing as 1/K, where K is the dimension of the transmitted signal.